How Dihalogens Catalyze Michael Addition Reactions.

We have quantum chemically analyzed the catalytic effect of dihalogen molecules (X2 =F2 , Cl2 , Br2 , and I2 ) on the aza-Michael addition of pyrrolidine and methyl acrylate using relativistic density functional theory and coupled-cluster theory. Our state-of-the-art computations reveal that activation barriers systematically decrease as one goes to heavier dihalogens, from 9.4 kcal mol-1 for F2 to 5.7 kcal mol-1 for I2 . Activation strain and bonding analyses identify an unexpected physical factor that controls the computed reactivity trends, namely, Pauli repulsion between the nucleophile and Michael acceptor. Thus, dihalogens do not accelerate Michael additions by the commonly accepted mechanism of an enhanced donor-acceptor [HOMO(nucleophile)-LUMO(Michael acceptor)] interaction, but instead through a diminished Pauli repulsion between the lone-pair of the nucleophile and the Michael acceptor's π-electron system.

The textbook Michael addition reaction, discovered by Arthur Michael in 1887,1 constitutes one of the most useful and synthetically powerful tools in organic chemistry.2 This is due to its ability to produce a new C−C bond in a single reaction step and with high or complete stereoselectivities (either diastereo‐ or enantioselectivity) when proper substrates and/or catalysts are used.3 For this reason, this process, as well as its heteroatom variants (e.g. aza‐ or oxa‐Michael additions), has been thoroughly applied toward the synthesis of a good number of target molecules including complex natural products4 and compounds relevant in biochemistry.5

It is well known that dihalogen molecules (X2), particularly molecular iodine, can be efficiently used as catalysts to significantly accelerate this fundamental reaction.6 It is widely accepted that the origin of the catalytic effect of these species, in not only this but also in related transformations,7 can be attributed to an attractive halogen bonding resulting from the interaction of the X2 molecules and the substrate. This mode of activation strongly resembles that found in typical Lewis acid catalyzed processes, where the catalysis is mostly governed by a favorable interaction involving the corresponding frontier molecular orbitals (FMOs), namely HOMO(nucleophile)–LUMO(Michael acceptor).8 Nevertheless, and despite recent studies on the mechanism of I2‐catalyzed Michael addition reactions,9 very little is known about the ultimate factors behind the catalytic activity of X2 molecules. For this reason, we decided to use state‐of‐the‐art computational methods10 to quantitatively unravel the nature of the catalytic power of these species.

To this end, we focused on the parent aza‐Michael reaction involving pyrrolidine and methyl acrylate (Scheme 1), which was experimentally studied by Borah and co‐workers.6d We considered both the uncatalyzed process and the analogous X2‐catalyzed reactions (where X2=F2, Cl2, Br2, and I2).

Scheme 1

Computationally analyzed Michael addition reactions.

First, we analyzed the nature and strength of the interaction between X2 and methyl acrylate in the initial methyl acrylate–X2 reactants 2 a–5 a using the energy decomposition analysis (EDA; see below) method (Table 1).11 The complexation energies are nearly exclusively determined by the interaction energies, which are all stabilizing and become stronger when moving down Group 17, ranging from −1.4 to −5.6 kcal mol−1 for 2 a to 5 a, respectively. The corresponding X⋅⋅⋅O distance becomes steadily longer in line with the increasing effective size of the halogen atom down Group 17. The electrostatic attractions are nearly twice as strong as the orbital interactions, which agrees with the electrostatic nature of the X−X⋅⋅⋅O=C noncovalent interaction. Despite this, the orbital term is not negligible, which suggests that the FMOs of methyl acrylate are strongly affected by the dihalogen molecule, particularly for the heavier halogens (see below).

Table 1

Energy decomposition analysis terms (in kcal mol−1) and X⋅⋅⋅O distance (in Å) computed on methyl acrylate–dihalogen adducts (2 a–5 a).[a]

System	ΔE	ΔE strain	ΔE int	ΔE Pauli	ΔV elstat	ΔE oi	r(X−X⋅⋅⋅O=C)
2 a: F2	−1.4	0.0	−1.4	1.3	−1.8	−0.9	2.701
3 a: Cl2	−3.4	0.0	−3.4	4.7	−5.5	−2.6	2.745
4 a: Br2	−5.1	0.1	−5.2	6.3	−7.4	−4.1	2.774
5 a: I2	−5.6	0.2	−5.8	8.9	−9.1	−4.6	2.880

[a] The two interacting fragments are X2 and methyl acrylate. Computed at the ZORA‐M06‐2X/TZ2P//M06‐2X/def2‐TZVP level.

As seen from Table 2, the uncatalyzed reaction has the highest barrier (11.2 kcal mol−1) and the least favorable reaction energy (−0.9 kcal mol−1). Coordination of X2 catalyst results in more favorable barrier heights that systematically decrease when descending Group 17 for X2, which is consistent with the experimental observations that bromine‐ and iodine‐based halogen‐bond donors are similarly active, whereas the corresponding chlorine derivatives are usually much less reactive.9 The trend of our computed DFT barriers and reaction energies agrees well with those calculated at the DLPNO‐CCSD(T)/def2‐TZVP//M06‐2X/def2‐TZVP level. The corresponding transition states are reached earlier and earlier when going from the uncatalyzed to the I2‐catalyzed reaction (see N⋅⋅⋅C distance in Table 2) and this results in systematically lower and lower barrier heights. This is fully consistent with the Hammond–Leffer postulate.12 For this reason, it is not surprising that a very good linear correlation is found when one plots the computed N⋅⋅⋅C bond‐forming distances in the transition states vs. the activation barriers (correlation coefficient of 0.995, see Figure S1). Gibbs free energy barriers follow the same trend in reactivity as barriers computed using the electronic energy (Figure S2).

Table 2

Energies (in kcal mol−1) and key geometry details (in Å) computed on transition state structures for reactions 1–5. HOMO–LUMO energy gap (in eV) based on energy minima of pyrrolidine and 1 a–5 a.

Reaction	X2	ΔE ≠	ΔE rxn	Δϵ HOMOpy–LUMO1–5	r(N⋅⋅⋅C)[b]
1	none	11.2 (12.7)	−0.9 (0.2)	7.4	1.829
2	F2	9.4 (11.7)	−1.3 (−0.4)	7.2	1.847
3	Cl2	7.6 (9.7)	1.7 (3.2)	6.6	1.867
4	Br2	6.2 (8.1)	0.9 (1.5)	6.0	1.882
5	I2	5.7 (7.1)	0.3 (0.4)	5.8	1.883

[a] All data computed at the M06‐2X/def2‐TZVP level unless otherwise specified. Energies in parentheses were computed at the DLPNO‐CCSD(T)/def2‐TZVP//M06‐2X/def2‐TZVP level. [b] Forming bond length between the nucleophilic N(py) and the terminal olefinic carbon atom of methyl acrylate (1 a–5 a).

As mentioned above, the catalytic effect of dihalogen molecules has been typically attributed to the enhancement of the HOMO(nucleophile)–LUMO(Michael acceptor) interaction, where LUMO refers to the empty π* orbital of the Michael acceptor.8 Figure 1 confirms that the computed electronic activation energies (ΔE ) correlate (R2=0.97) with the Δϵ(HOMO | LUMO) which, at first sight, seems to be in line with this traditional view on the origin of the computed reactivity trend.

Figure 1

Activation barriers for reactions of 1 a–5 a with pyrrolidine (py) versus the reactants’ HOMO–LUMO gap Δϵ, computed at the M06‐2X/def2‐TZVP level.

We next turned to the activation strain model (ASM) of reactivity13 to gain a deeper and quantitative insight into the physical factors leading to the enhanced reactivity of X2‐catalyzed Michael addition reactions. This analysis decomposes the electronic energy (ΔE) into two terms: the strain (ΔE strain) that results from the distortion of the individual reactants and the interaction (ΔE int) between the deformed reactants along the reaction coordinate, defined in this case by the C=C bond elongation in methyl acrylate. This geometrical parameter is critically involved in the reaction and undergoes a well‐defined change over the course of the Michael addition.14 Figure 2 a shows the corresponding activation strain diagrams (ASDs) from the reactant complex to the transition states for the uncatalyzed (1) and X2‐catalyzed (2–5) Michael addition reactions. The accelerated reactivity of the X2‐catalyzed reactions originates primarily from a more stabilizing interaction energy along the entire reaction coordinate and also from a less destabilizing strain (albeit to a lesser extent). The interaction energy becomes increasingly more stabilizing in the order of X2=noneCl2ctly the same trend as the activation barriers. Thus, the reactivity trends is caused by the trend in the interaction between the two reactants. The strain energies for the X2‐catalyzed reactions are similar along the reaction coordinate but are less destabilizing compared to the uncatalyzed reaction.

Figure 2

a) Activation strain analyses of the Michael addition reactions between py and 1 a–5 a and b) energy decomposition analyses of the least (1 a, black lines) and most reactive (5 a, red lines) substrates computed at the ZORA‐M06‐2X/TZ2P//M06‐2X/def2‐TZVP level.

Since the interaction energy plays such a critical role in the observed reactivity trends, the different contributors to the interaction energy were analyzed by applying our canonical energy decomposition analysis (EDA) which quantifies the various features in the bonding mechanism.11 Thus, the interaction ΔE int between the reactants is further decomposed into three energy terms that can be associated with the following physical factors: classical electrostatic interaction (ΔV elstat), Pauli repulsive orbital interactions (ΔE Pauli) between closed‐shell orbitals (actually, between same‐spin electrons) which is responsible for steric repulsion,15 and stabilizing orbital attractions (ΔE oi) that account, among others, for HOMO–LUMO interactions. For the purpose of clarity, only the corresponding energy decomposition analysis (EDA) results for the uncatalyzed (1) and I2‐catalyzed (5) reactions are shown in Figure 2 b as these reactions represent the slowest and fastest reactions, respectively. Quite unexpectedly, we find that the process involving 5 a goes with a stronger interaction energy due exclusively to a much less destabilizing Pauli repulsion as compared to that involving 1 a. Indeed, both the electrostatic and orbital interactions in the process involving 5 a are even less stabilizing (not more stabilizing as one might have expected) than those for the reaction involving 1 a, despite the former exhibiting a more favorable (smaller) donor–acceptor FMO energy gap.

Clearly, the ΔE Pauli term determines the trend in interaction energies and, ultimately, in activation barriers for these reactions. This finding is unprecedented and constitutes a novel physical mechanism behind the catalytic role of dihalogen molecules in the studied Michael addition reactions.16

To understand the origin of the less destabilizing Pauli repulsion for the I2‐catalyzed reaction, which results in the most favorable interaction energy and thus the lowest activation barrier of all the studied reactions, we performed a Kohn–Sham molecular orbital (KS‐MO) analysis.17 We have quantified the most significant four‐electron interactions between filled molecular orbitals18 of pyrrolidine (py) with 1 a–5 a at consistent geometries with a C=C bond length stretch of 0.062 Å (Figure 3 a). Analysis at a consistent point on the reaction coordinate, that is both close in geometry and energy to the actual TS, rather than at the transition state alone, ensures that the results are not skewed by the position of the transition state.13 The π‐MO involved in this four‐electron interaction is the HOMO for reactions 1 and 2, the HOMO and HOMO−1 for 3, the HOMO−2 for 4, and the HOMO−3 for 5. For the heavier dihalogens in 4 a and 5 a, the X2 lone pairs are higher‐lying19 than the key π‐FMO in 1 a, and for this reason, the π‐MO in the adducts is lower in energy than the HOMO. The orbital overlap between the π‐MO and lone pair π‐HOMO is largest and most destabilizing for the uncatalyzed reaction (1) (S=0.17) and smallest and least destabilizing for the I2‐catalyzed reaction (5) (S=0.10) (see Figure 3 b for the involved MOs). The polarization of the π‐MO away from the C=C double bond by the dihalogen is the reason for the decreased HOMO|π‐MO overlap. Weak, but non‐negligible, donor–acceptor interactions between the σ*‐X2 and the π‐HOMO of methyl acrylate (see Table 1) cause charge transfer from methyl acrylate to the X2 moiety and results in less amplitude on the carbon atom directly involved in the Michael addition (schematically illustrated in Scheme 2). This follows from the expected trend of Lewis acidity of halogen atoms along the series F>Cl>Br>I.20 Thus, the extent of polarization induced by the halogen is almost negligible for 2 a, but is more significant for 5 a as clearly viewed when comparing the corresponding π‐density of the C=C bond (see Figure 3 b).

Figure 3

a) Molecular orbital diagram and the most significant occupied orbital overlaps of the Michael addition reactions between 1 a and 5 a with py and b) key occupied orbitals (isovalue=0.07) computed at the ZORA‐M06‐2X/TZ2P//M06‐2X/def2‐TZVP level.

Scheme 2

Schematic orbital interaction diagram between the π‐HOMO of methyl acrylate and the σ*‐LUMO of X2 for 2 a (X2=F2) and 5 a (X2=I2) resulting in a smaller amplitude of the resulting π orbital on the terminal carbon atom involved in the forming C−N bond.

We finally explored our counterintuitive EDA finding that the strength of the orbital interactions actually become weaker for the I2‐catalyzed (5) reaction than for the uncatalyzed (1) reaction, although the former exhibits a more favorable FMO energy gap. We have computed the frontier molecular orbital (FMO) gaps and overlaps, once again, on consistent geometries with a C=C bond length stretch of 0.062 Å (Figure 4). As expected, the FMO energy gaps for the HOMO–LUMO interaction decrease and range from 6.1 to 5.4 eV for the uncatalyzed and the I2‐catalyzed reaction, respectively. Despite the more favorable FMO gaps, the strength of the orbital interactions actually becomes less stabilizing for the X2‐catalyzed reactions due to poorer orbital overlap. The computed orbital overlap decreases significantly from S=0.19 to 0.13 for reactions 1 and 5, respectively. There are two FMO interactions for reaction 4 that involve both the nearly degenerate LUMO (S=0.10) and LUMO+1 (S=0.15) virtual π* orbitals. Thus, it is the poorer FMO orbital overlaps that arise, again, from the polarization of the LUMO away from the C=C double bond by the dihalogen. This polarization‐induced weakening of the FMO orbital overlaps effectively counteracts the more favorable (smaller) energy gaps and results in less stabilizing orbital interactions when descending Group 17 for the X2.

Figure 4

Molecular orbital diagram with the orbital energy gap and overlap of the HOMO‐π‐MO interaction for the Michael addition reactions 1–5 computed at the ZORA‐M06‐2X/TZ2P//M06‐2X/def2‐TZVP level.

In conclusion, our ASM‐EDA study shows that the dihalogen catalysis of the considered Michael additions is brought about by a hitherto unknown electronic mechanism: we find that it is not caused by an effective enhancement of the Lewis acidity of the Michael acceptor leading to an enhanced donor–acceptor [HOMO(nucleophile)–LUMO(Michael acceptor)] interaction. Instead, the decrease in barrier when X2 binds to the carbonylic oxygen of the Michael acceptor is due to the concomitant polarization of its conjugated π‐system away from the electrophilic carbon atom. This has the effect of reducing the four‐electron (Pauli) repulsion with the lone pair of the nucleophile. This reduction in repulsion causes an enhancement of the overall nucleophile–Michael acceptor interaction and thus the observed lowering of the reaction barrier.

Conflict of interest

The authors declare no conflict of interest.

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